Apparatus and method for measuring nuclear spin-lattice relaxation time (t1) by tone-burst modulation

ABSTRACT

The static field of an NMR spectrometer is modulated by a series of repeated tone bursts of an audio wave of triangular or sinusoidal form with the bursts separated by periods of at least four times the spin-lattice relaxation time T1. The static field has a value such that the superimposed modulation causes field strength excursions equal distances above and below the magnetic resonance value. The spectrometer output signals produced by the passages through the resonance value are displayed by an oscilloscope having its horizontal sweep synchronized with the start of each tone burst. The value of T1 is calculated from measurements made on the recorded oscilloscope display.

United ates tent [54] APPARATUS AND METHOD FOR MEASURING NUCLEARSPIN-LATTICE RELAXATION TIME (T BY TONE-BURST MODULATION 5 Claims, 2Drawing Figs.

[52] U.S. Cl 324/05 S. Meiboom & D. Gill Modified Spin Echo Method forMeasuring Nuclear Relaxation Times Rev. of Scientific Instruments 29(8)Aug. 1958 pp. 68869l.

Primary ExaminerMichael J. Lynch Attorneys-Harry A. Herbert, Jr. andJames S. Shannon ABSTRACT: The static field of an NMR spectrometer ismodulated by a series of repeated tone bursts of an audio wave oftriangular or sinusoidal form with the bursts separated by periods of atleast four times the spin-lattice relaxation time T The static field hasa value such that the superimposed modulation causes field strengthexcursions equal distances (Lit) above and below the magnetic resonancevalue. The spec- [5 6] References Cited OTHER REFERENCES L. MallingField Pulses Produce Nuclear Spin Echoes Electronics-June 1954 -pp. 134-137.

trometer output signals produced by the passages through the resonancevalue are displayed by an oscilloscope having its horizontal sweepsynchronized with the start of each tone burst. The value of T iscalculated from measurements made on the recorded oscilloscope display.

PATENTED HAR 2 I97! was new P r 05c. A-

SHEET 1 OF 2 Tame-sues)" Gnu-47 2 APPARATUS AND METHOD FOR MEASURINGNUCLEAR SPIN-LATTICE RELAXATION TIME (T BY TONE-BURST MODULATIONBACKGROUND OF THE INVENTION This invention relates to NMR (nuclearmagnetic resonance) and particularly to the measurement of nuclearspin-lattice relaxation times in liquids and solids using continuouswave NMR spectroscopy.

In studying the properties of matter, such as the electrical propertiesof semiconductors for example, useful information is provided by thenuclear spin-lattice relaxation time, i.e., the time constant T of theexponential function in accordance with which a sample in a strongstatic magnetic field approaches a state of thermal equilibrium betweenthe nuclear spin system and the lattice. The relaxation process isrepresented by the equation M(t) the magnetic moment of the sample attime t,

M, the magnetic moment at the start of relaxation which may be zero, and

M the magnetic moment at equilibrium.

Continuous wave spectroscopy is usedprimarily for lineshape studiesalthough relaxation investigations are sometimes carried out, usually byone of three methods: (1) a direct method in which the recovery of thesignal is observed in a weak RF field H after saturation in a strong H(2) a progressive saturation method in which the steady state signal ismeasured as a function of RF field strength; and (3) a transient method,in which the spin system is saturated at resonance, quickly moved offresonance for a time t, and then swept back through the resonance toobserve the magnetization recovery in time 1. Method (1) has thedisadvantage that the relaxation is occurring in the presence of Hrequiring a correction factor; also H must be switched from a high to alow value. Method (2) requires an accurate measurement of H and is onlyuseful for simple line shapes, either Lorentzian or Gaussian. Method (3)is excellent for long relaxation times seconds or greater) where thespin system is easily saturated, but is not readily adaptable to measureshorter times. An existing method which gives reliable results for bothlong and short relaxation times is the pulsed NMR technique; however,this method requires a different spectrometer and usually is lesssensitive to weak-signaled spin systems.

SUMMARY OF THE INVENTION The method of measuring T to be described andwhich constitutes the invention can be practiced with a standardcontinuous wave NMR spectrometer with a minimum of modification andadded equipment. Briefly, the modification consists in adding atone-burst generator in combination with a triangular (or sinusoidal)wave generator to provide a series of audio frequency tone bursts to theDC magnetic field modulating coils of the NMR spectrometer. The tonebursts contain equal numbers of the cycles of the audio wave and areseparated by intervals of at least 4T,. The DC field is set at a valuesufficiently below the nuclear magnetic resonance value that thesuperimposed modulation carries the field to a point equally above theresonance value and back to the set value in each cycle of themodulating wave, the field passing twice through the resonance value ineach cycle. The spectrometer signals resulting from the passages throughthe resonance value decrease in magnitude exponentially and aredisplayed on an oscilloscope having a linear horizontal sweepsynchronized with the start of each tone burst. The value of T iscalculated from measurements made on the recorded oscilloscope display.The calculation can be made from the record of a single tone burst;however, where signal enhancement is needed, automatic, unattendedoperation is possible over a large number of tone bursts using atime-averaging computer, a repetitive-scan storage oscilloscope, orother suitable device to sum the signals produced by each tone burst.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 shows a NMR spectrometerarranged for spin-lattice relaxation measurement in accordance with theinvention; and

FIG. 2 shows waveforms occurring in FIG. 1.

DETAILED DESCRIPTION OF THE INVENTION Referring to FIG. 1, the standardcontinuous wave NMR spectrometer employed in relaxation measurements inacv cordance with the invention will be described first. The sample tobe analyzed is supported by a suitable sample holder 1 in the center ofa strong static or DC magnetic field H established between the polefaces 2 and 3 of an electromagnet having energizing coils 4 and 5. Themagnetizing current is supplied by source 6 and is adjustable so thatthe field strength can be varied. This field is usually referred to asthe polarizing field. Two-section coil 7, energized from variablefrequency RF oscillator 8, is provided for the application of a RFmagnetic field to the sample. This coil is usually referred to as thetransmitting coil. Coil 9, which has the sample at its center, isusually referred to as the receiving coil. The axes of coils 7 and 9 liein a plane normal to the direction of field H, and intersect at a pointthat is preferably at the center of the sample.

A Faraday shield (not shown) is usually provided between coils 7 and 9to reduce electrostatic coupling to a minimum. Since coils 7 and 9 areat right angles the magnetic coupling between them approaches zero.However, in accordance with standard practice, it is necessary tointroduce a certain amount of leakage coupling between the two coilsthat is controllable in magnitude and phase in order to establishoperation of the NMR spectrometer in either the V-mode (absorption mode)or the U-mode (dispersion mode). This is usually accomplished byintroducing small highly conductive discs and small shorted resistiveloops into the vicinity of the coils by means of paddles, the discscontrolling the V-mode component and the resistive loops the U-modecomponent in the receiving coil 9. Since this is standard practice inNMR spectrometers, the paddles for controlling the leakage coupling arenot shown in FIG. 1 in order to simplify the drawing. In practicing theinvention, the leakage is preferably adjusted for V- mode or absorptionmode operation in which the signal produced in receiving coil 9 peaks atnuclear magnetic resonance.

Finally, the NMR spectrometer is provided with a pair ofseries-connected coils 10 and 11 concentric with an axis passing throughthe point of intersection of the axes of coils 7 and 9 and normal tothese axes. The purpose of these coils is to modulate the steady field Hproduced by the large electromagnet. In conventional use of thespectrometer, and similarly in its use in the invention, these coilsserve to sweep the field back and forth over a small range centered onthe resonance value.

The illustration of the NMR spectrometer structure in FIG. 1 is intendedto show clearly the component parts and their relation to each otherrather than to show an actual construction to scale. Coils 7, 9, 10, and11 are in actual practice mounted in a single structure called a probewhich is adapted to receive the sample holder 1. The probe has athickness 'of about 1 inch so that it can be inserted in an onlyslightly wider airgap between pole faces 2 and 3.

In order to use a continuous wave NMR spectrometer for the measurementof spin-lattice relaxation times in accordance with the invention, atone-burst audio frequency modulation is added to the steady magneticfield H, in the following manner: A triangular waveform generator 12produces a triangular wave of voltage, such as shown by waveform A ofFIG. 2, which is applied as an input signal to tone-burst generator 13.The tone-burst generator acts to alternately pass the input wave for aspecified number of its cycles and to block passage of the wave for apredetermined number of its cycles, depending upon the setting of thecycles-on control I4 and the cycles-off control 15, respectively, of thecounting and timing circuits 16. The alternate passing and blocking ofthe wave A is accomplished by gate 17 which acts as an on-off switch.When switch 17 is on, wave A is passed through the switch and outputamplifier 18 to the output circuit 19 of the tone-burst generator; whenofF there is no output from the tone-burst generator. The counting andtiming circuits 16 are synchronized with the wave A by trigger pulsesderived from this wave by trigger circuit 20 and shown in waveform B ofFIG. 2. By means of trigger level control 21 of circuit 20, the triggerpulses can be made to occur at any selected voltage of wave A. Forpurposes of the invention, this control is preferably set for triggerpulses to occur at the lowest value of wave A, as shown in FIG. 2. Theoperation of gate or switch 17 is controlled by a gate pulse generatedby circuit 16 and shown, after amplification and inversion in gatedriver amplifier 22, by waveform C of FIG. 2. In the specific exampleshown, it is seen that eight full cycles of wave A are allowed to passand 15 cycles are blocked from passage. The resulting 8- cycle toneburst is applied to the input of zero-damping amplifier 23 which drivesthe modulating coils l and 11. The design of the amplifier is such thatthe current through the modulating coils is proportional to theamplifier input voltage. The zero point of the output of amplifier 23 isso adjusted that the current through coils l0 and 11 flows in only onedirection, or, in other words, varies between zero and a maximum valueof one sign as shown by waveform D of FIG. 2. Therefore, if the fieldproduced by I flowing in coils l0 and 11 has a value 2yH and the steadyfield H, is adjusted at source 6 to have a value H,=H,,Awhere H is theresonance value of H then H, increases from H through H to the value H,+2AH and decreases from this value through H to the starting value H, ineach cycle of the tone burst, as shown by waveform F in FIG. 2. As aresult the field passes through H twice in each cycle of the tone burstand these passages are separated equally in time by the intervall/2f,,,.

The tone-burst generator 13 also provides means for synchronizing thehorizontal sweep of an oscilloscope with the tone burst. For thispurpose the output pulse of circuit 16 is also applied to asynchronizing signal amplifier 24 the output of which is of the samewaveform as the gate pulse output of amplifier 22 and therefore may alsobe represented by waveform C of FIG. 2. This pulse is applied to thehorizontal synchronizing signal input of oscilloscope 25 and causes itshorizontal sweep to be initiated in coincidence with the leadingnegative-going edge of the pulse, and therefore in coincidence with thestart of the tone burst, as shown by waveform E of FIG. 2.

Tone-burst generators such as that shown in block form in FIG. 1 arewell known in the art and available commercially. An example is theGeneral Radio, Type l396-B, Tone-Burst Generator.

The operation of the apparatus of FIG. I and the mannerof using theapparatus to derive the spin-lattice relaxation time T ofa sample are asfollows:

As is known in the NMR art and as described in the literature on thesubject, for example, Nuclear Magnetic Resonance by E. R. Andrew,Cambridge University Press, 1958, nuclear magnetic resonance occurs inthe sample when the angular velocity of the RF energization applied tothe transmitting coil, and therefore the angular velocity to, of the RFfield H produced by this energization, equals the angular velocity (0,,of the precession of the vector representing the magnetic moment of thesample about the direction of the polarizing magnetic field H, in whichthe sample is immersed. The angular velocity to of the precessing vectoris given by the relation where H, is the strength of the polarizingmagnetic field and 'y is the gyromagnetic ratio, or the ratio of themagnetic moment of the nucleus to its spin moment. Thus, resonanceoccurs when a), of the RF energization of coil 7 equals m The precessingmagnetic moment of the sample induces a voltage in receiving coil 9which is small for nonresonant conditions but increases rapidly as w,approaches 0),, and, for V- mode operation, attains a peak value at (Bf-0),,- It is the usual practice, and the practice in this case, to holdw, of the RF field constant at a suitable value and vary the polarizingfield H, to achieve the resonant condition, as indicated by peak outputfrom receiving coil 9, at

. In order to display the output of the NMR spectrometer on the screenof oscilloscope 25, the RF voltage induced in receiving coil 9 is firstamplified by a suitable RF amplifier 26, rectified in detector 27, and,after further amplification of the detected signal in amplifier 28,applied to the vertical deflection circuit of the oscilloscope.

Assuming, with reference to the modulated polarizing field waveform F ofFIG. 2, that H0= =HR 'Y the resonance value of the polarizing field, theNMR spectrometer is swept through the resonant condition sixteen timesduring each 8-cycle tone burst applied to modulating coils l0 and 11.The resulting spectrometer output signal during the tone burst, asdisplayed on the oscilloscope, is illustrated by waveform G of FIG. 2.

As seen from waveform G, the first resonant peak, occuring at n=0, hasthe maximum magnitude and the subsequent peaks decline exponentially inmagnitude T,, minimum value is reached at n=9 or 10 in the illustratedexample. The reason for this is as follows: As stated earlier theinterval between tone bursts is made at least as long as 4T so that thesample has sufficient time during this interval to reach substantially astate of thermal equilibrium between the nuclear spin system and thelattice in the presence of the off-resonance value H, of the polarizingfield H and the presence of the RF field H,. In this relaxed state ofthe sample, the maximum number of nuclear magnetic moments havecomponents lying in the direction of the polarizing field H,,. Duringresonance the effect of the RF field H, is to rotate a number of thenuclear moments into the plane of the axes of coils 7 and 9. Since thenumber rotated depends upon a probability of such rotation taking place,the maximum number are rotated when the maximum number of nuclei havetheir moments aligned with H,,. Therefore, the maximum number arerotated at the first pass through resonance after a state of equilibriumhas been attained, and, since the rotated moments are responsible forthe increase in the signal induced in coil 9 at resonance, the maximumoutput signal occurs at this time. In the interval l/2f,,, betweenresonances some spin-lattice relaxation occurs but there is insufficienttime for all the moments rotated to return to alignment with HTherefore, at the second pass through resonance, the number of momentsin alignment with H is less than at the first pass so that, with thesame probability, fewer are rotated and the output signal is less. Itshould be stated at this point that those rotated at resonance quicklylose their phase coherence in the interval between resonances due tospin-spin relaxation and contribute no signal at the succeedingresonance. The output signal continues to decline in the above manneruntil, at about the 9th or 10th pass through resonance in the exampleillustrated by waveform G, the number of moments returning to alignmentwith H during the interval between resonances equals the number rotatedfrom alignment, with the result that the population of aligned momentsremains constant for subsequent passes and the output signal stabilizesat a minimum value.

Since T is not likely to be known, an adequately long interval betweentone bursts, or off interval, can be determined experimentally by notingthe value M of the first resonance following an interval obviously longenough for the sample to attain spin-lattice equilibrium and reducingthis interval until a smaller value of M is obtained. An intervalslightly larger than the value at which a reduced M, is first noted maythen be set into the tone-burst generator 13.

The tracing shown as waveform G in FIG. 2 is a copy of one actuallyobtained in the process of measuring the value of T for the F" in a CaFcrystal by the described method. The parameters in this case were:

H 0.306; 2AH 506; f, 30H and H, 10,9006. The value of T computed in themanner described below, was 0.12 seconds. With an off time of cycles inFIG. 2 and a triangular wave period of 1/30 second, the off time is .50seconds, which is slightly more than the 4T, interval required.

In order to compute T from the recorded display on the oscilloscope, ofwhich waveform G of FIG. 2 is an example, the following steps arecarried out:

I. A plot of log. (M -M) vs. n is made on log paper, the

highest value of n being that at which the minimum output signal,designated M 9 is first attained. The values of M are measured directlyfrom the recorded display. The best straight line is drawn through theplotted points and its intercept I at n=0 is measured. The slope S ofthis line is also determined from the graph.

2. The values of I and S determined above, together with the value of 1:log

The derivation of the above formula is given in our paper entitledNuclear Spin-Lattice Relaxation Measurements by Tone-Burst Modulation,appearing in Physical Review Letters, Vol. 20, No. 18, Apr. 29, 1968,page 987-989.

In practicing the above method, in addition to providing a sufficientoff interval between tone bursts to permit the magnetization of thesample to fully recover, as explained above, the H modulating fieldstrength ZAH should be much larger than the line width, or width of theresonance curve, 8H; the combination of RF field strength H andmodulating frequency f,, are so adjusted as to lead to a nonadiabaticsignal response; and the period of the H, modulation should be much lessthan the expected value of T The three conditions may be expressed asfollows:

the gyromagnetic ratio.

We claim:

1. Nuclear magnetic resonance apparatus comprising: a transmitting coiland a receiving coil having axes at right angles to each other andintersecting at a point within the confines of each coil; means forsupporting a sample to be analyzed substantially at said point ofintersection; means for continuously applying radio frequency energy ofconstant amplitude and frequency to the transmitting coil for subjectingthe sample to an alternating radio frequency magnetic field of constantamplitude and frequency directed along the axis of the coil; means forproducing in the region of said sample a continuous unidirectionalpolarizing magnetic field having a direction normal to the plane of saidintersecting axes and having a fixed value differing slightly from thevalue required for nuclear magnetic resonance in said sample at thefrequency of said radio frequency field; means operative during the onperiods of a series of alternate fon and off" periods for superimposingon said fixed polarizing field and in alignment therewith a relativelyweak additional unidirectional field alternating between maximum andminimum values in accordance with a symmetrical nonrectangularmodulating wave the period of which is very much less than the timerequired for the sample to obtain spin-lattice equilibrium, saidadditional field being of such magnitude and polarity that the resultingtotal polarizing field has an alternating component centered on saidresonance value; a recorder having a constant velocity sweep forrecording the amplitude of a signal as a function of time; means forinitiating the start of the recorder sweep at the beginning of each onperiod; and means coupled to said receiving coil for producing a signalproportional to the amplitude of the voltage induced in the coil by theprecessing magnetic moment of the sample and for applying the signal tosaid recorder.

2. Apparatus as claimed in claim 1 in which the phase of the leakagecoupling between the transmitting coil and the receiving coil is suchthat the leakage signal in the receiving coil is in phase with thenuclear magnetic resonance signal in this coil so as to provide foroperation in the absorption mode.

3. Apparatus as claimed in claim 2 in which the length of the on" periodis sufficient to include as many cycles of said modulating wave asnecessary to achieve a stableminimum amplitude in the signal applied tothe recorder and the length of the off period is sufficient forsubstantially complete spin-lattice equilibrium to be attained in thesample in the presence of said fixed polarizing field and said ratiofrequency field.

4. Apparatus as claimed in claim 3 in which the waveform of saidmodulating wave is triangular.

5. Apparatus as claimed in claim 1 in which the minimum value of saidadditional field is zero.

1. Nuclear magnetic resonance apparatus comprising: a transmitting coiland a receiving coil having axes at right angles to each other andintersecting at a point within the confines of each coil; means forsupporting a sample to be analyzed substantially at said point ofintersection; means for continuously applying radio frequency energy ofconstant amplitude and frequency to the transmitting coil for subjectingthe sample to an alternating radio frequency magnetic field of constantamplitude and frequency directed along the axis of the coil; means forproducing in the region of said sample a continuous unidirectionalpolarizing magnetic field having a direction normal to the plane of saidintersecting axes and having a fixed value differing slightly from thevalue required for nuclear magnetic resonance in said sample at thefrequency of said radio frequency field; means operative during the''''on'''' periods of a series of alternate ''''on'''' and ''''off''''periods for superimposing on said fixed polarizing field and inalignment therewith a relatively weak additional unidirectional fieldalternating between maximum and minimum values in accordance with asymmetrical nonrectangular modulating wave the period of which is verymuch less than the time required for the sample to obtain spin-latticeequilibrium, said additional field being of such magnitude and polaritythat the resulting total polarizing field has an alternating componentcentered on said resonance value; a recorder having a constant velocitysweep for recording the amplitude of a signal as a function of time;means for initiating the start of the recorder sweep at the beginning ofeach ''''on'''' period; and means coupled to said receiving coil forproducing a signal proportional to the amplitude of the voltage inducedin the coil by the precessing magnetic moment of the sample and forapplying the signal to said recorder.
 2. Apparatus as claimed in claim 1in which the phase of the leakage coupling between the transmitting coiland the receiving coil is such that the leakage signal in the receivingcoil is in phase with the nuclear magnetic resonance signal in this coilso as to provide for operation in the absorption mode.
 3. Apparatus asclaimed in claim 2 in which the length of the ''''on'''' period issufficient to include as many cycles of said modulating wave asnecessary to achieve a stable minimum ampLitude in the signal applied tothe recorder and the length of the ''''off'''' period is sufficient forsubstantially complete spin-lattice equilibrium to be attained in thesample in the presence of said fixed polarizing field and said ratiofrequency field.
 4. Apparatus as claimed in claim 3 in which thewaveform of said modulating wave is triangular.
 5. Apparatus as claimedin claim 1 in which the minimum value of said additional field is zero.